Question

Select the correct answer.How would you write this expression as a sum or difference?log, (VI · y)

Answer 1

First, we can see in the alternatives that the base of the logarithm is not changed, so we don't need to bother with that.

Now, a multiplication inside a logarithm has the following property:

`\log _b(a\cdot c)=\log _b(a)+\log _b(c)`

Applying that to the given expression, we have:

`\log _3(\sqrt[5]{x}\cdot y)=\log _3(\sqrt[5]{x})+\log _3y`

Now, we can rewrite the root in the radical form:

`\sqrt[5]{x}=x^{(1)/(5)}`

To get:

`\log _3(x^{(1)/(5)})+\log _3y`

We did that so we can use the following property:

`\log _b(a^c)=c\cdot\log _ba`

Let's do that:

`(1)/(5)\log _3x+\log _3y`

And that is the answer.